Results 91 to 100 of about 147 (114)
Improved Bounds for the Excluded-Minor Approximation of Treedepth [PDF]
SIAM Journal on Discrete Mathematics, 2021 Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays a major role in the theory of sparse graph classes. We show that there exists a constant $C$ such that for every positive integers $a,b$ and a graph $G$, if the treedepth of $G$ is at least $Cab$, then the treewidth of $G$ is at least $a$ or $G$ contains a subcubic (
Wojciech Czerwinski +2 more
exaly +8 more sources
Treedepth vs Circumference [PDF]
Combinatorica, 2023 The circumference of a graph $G$ is the length of a longest cycle in $G$, or $+\infty$ if $G$ has no cycle. Birmelé (2003) showed that the treewidth of a graph $G$ is at most its circumference minus $1$. We strengthen this result for $2$-connected graphs as follows: If $G$ is $2$-connected, then its treedepth is at most its circumference.
Gwenael Joret +2 more
exaly +6 more sources
Polynomial Treedepth Bounds in Linear Colorings [PDF]
Algorithmica, 2020 AbstractLow-treedepth colorings are an important tool for algorithms that exploit structure in classes of bounded expansion; they guarantee subgraphs that use few colors have bounded treedepth. These colorings have an implicit tradeoff between the total number of colors used and the treedepth bound, and prior empirical work suggests that the former ...
Jeremy Kun +2 more
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Tight Bound on Treedepth in Terms of Pathwidth and Longest Path [PDF]
Combinatorica, 2023 We show that every graph with pathwidth strictly less than $a$ that contains no path on $2^b$ vertices as a subgraph has treedepth at most $10ab$. The bound is best possible up to a constant factor.
Gwenael Joret +2 more
exaly +6 more sources
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On the Lossy Kernelization for Connected Treedepth Deletion Set
Lecture Notes in Computer Science, 2022Eduard Eiben +2 more
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Exploring the Gap Between Treedepth and Vertex Cover Through Vertex Integrity [PDF]
Lecture Notes in Computer Science, 2021 30 pages, 5 figures, CIAC ...
Tatsuya Gima +2 more
exaly +3 more sources
MaxSAT-Based Postprocessing for Treedepth
Lecture Notes in Computer Science, 2020Treedepth is an increasingly popular graph invariant. Many NP-hard combinatorial problems can be solved efficiently on graphs of bounded treedepth. Since the exact computation of treedepth is itself NP-hard, recent research has focused on the development of heuristics that compute good upper bounds on the treedepth.
Stefan Szeider +2 more
exaly +2 more sources
A Heuristic Approach to the Treedepth Decomposition Problem for Large Graphs
Lecture Notes in Computer Science, 2021In this article, we describe algorithms and techniques used in the method ExTREEm for the treedepth decomposition problem. ExTREEm won the heuristic track of the 5th Parameterized Algorithms and Computational Experiments Challenge (PACE 2020). It searches for a minimum-height treedepth decomposition of a graph via computing graph separators.
Sylwester Swat +2 more
exaly +2 more sources
A Faster Parameterized Algorithm for Treedepth [PDF]
Lecture Notes in Computer Science, 2014 The width measure \emph{treedepth}, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. We present an algorithm which---given as input an $n$-vertex graph, a tree decomposition of the graph of width $w$, and an integer $t$---decides Treedepth, i.e ...
Felix Reidl +2 more
exaly +3 more sources